Hyperloglog can be expressed in three functions Initialize, Union, and Card. Sketches are easily merged by populating a new set of registers with the element-wise max values for each register. To extract the estimate, the algorithm finds the harmonic mean of \(2^{M[m]}\)  for each of the the \(m\)  registers. This mean estimates the cardinality of the set divided by \(m\) . To find the estimated cardinality we multiply by \(m\)  and \(\alpha _m\) . \(\alpha _m\)  is used to correct multiplicative bias. Additional information about the computation of \(\alpha _m\)  along with techniques to improve the estimate can be found in [1]}, [2]}. The full algorithm is presented in Algorithm REF .
